The Kelly Criterion: Position Sizing for the Experienced Day Trader

When it comes to managing risk in trading, the real challenge isn’t just about choosing good setups, it’s about knowing how much to risk when the edge is in your favour. This is where the Kelly Criterion comes in. Originally designed for gambling, it has found a home in quantitative finance and advanced trading but it’s not something for beginners.

Let’s break it down simply and then look at how it applies to day trading, and in particular, how we at LepusProp approach it with the caution it deserves.

🔹 What Is the Kelly Criterion?

The Kelly Criterion is a formula used to calculate the optimal size of a bet or trade based on your edge. The formula aims to maximise capital growth over time without risking ruin. Think of it as a mathematical guide for how much of your capital to put on the line — not too much to blow up, and not too little to stagnate.

In its simplest trading form, it looks like this:

f* = W - (L / R)

Where:

·         W = Win rate (as a decimal)

·         L = Loss rate (1 – W)

·         R = Reward-to-risk ratio (average win / average loss)

·         f* = Fraction of capital to risk on each trade

🔹 From Blackjack to the Markets

The Kelly Criterion was first used in gambling, notably by card counters in blackjack who had a measurable edge. In a casino, the outcomes are relatively fixed — the probabilities and payoffs are known and the playing field is clearly defined. In such an environment, the Kelly bet could be used almost mechanically to scale bets with confidence.

But in day trading, the environment is far more dynamic. You’re dealing with changing volatility, economic news, psychological traps, and imperfect data. So while the formula can still offer a valuable insight into position sizing, it must be applied far more cautiously.

🔹 Applying the Kelly Criterion in Day Trading

Here’s a worked example. Suppose your system has the following stats:

• Win rate: 55% (0.55)

• Loss rate: 45% (0.45)

• Reward-to-risk ratio: 1.5

Plugging into the formula:

f* = 0.55 - (0.45 / 1.5) = 0.25

This tells you to risk 25% of your capital per trade. Now, that might make sense in a casino where the rules and the environment never change. But in the trading world? That level of risk is far too aggressive.

At Lepus Proprietary Trading, we treat the Kelly Criterion as an upper boundary and not a target. In fact, we often operate on a 10% Kelly model. In other words, if the formula says 25%, we might risk just 2.5%, and only in highly probable, proven setups. This aligns with what Tom Hougaard describes in The Best Loser Wins — that we increase size not blindly, but only when we are already in profit or trading with momentum in our favour. How is this done, simply scale in to winning trades with fixed position sizing.

🔹 When Might You Use a Higher Fraction?

As a general rule, only advanced traders with deep knowledge of their edge should apply even a reduced Kelly strategy. It's not for new traders, period. You must have:

• A fully tested and well-documented trading system

• Reliable performance data (win rate, system R)

• Confidence and experience in executing under pressure

Situations where we might consider modestly increasing size include:

• Regression touches (e.g. Lorentz regression points)

• VWAP test

• Trades already in profit — adding to a winning position in line with Kelly dynamics

• Open Drive during a high-volume session open

These may be high-confidence setups where we may have every reason to trust our edge.

🔹 The Key Point: Use It Cautiously, If At All

While the Kelly Criterion is elegant in theory, the real world isn’t a probability lab. Noise, slippage, and changing market conditions all chip away at the assumptions behind the math. That’s why we scale down. A 10% Kelly approach is plenty for experienced traders looking to responsibly increase returns during high-probability moments — without overstretching risk.

And again, let us be clear: this is an advanced technique. For most traders — especially those still developing their systems — simple fixed fractional sizing or volatility-adjusted risk is safer, more consistent, and frankly, more forgiving.

✅ Final Thoughts

The Kelly Criterion is a powerful tool in the hands of a seasoned trader, but it must be treated with respect. It’s about knowing when to press, not pressing every time. As with all elements of trading, size must follow structure, discipline, and edge — not emotion or impulse.

If you’re not sure whether you have an edge — you don’t. And that’s okay. Build your system, gather the data, and the time to consider techniques like this will come.

For now, focus on consistency.